We will utilize the following result of [1]}.
[Strong Coresets]
Let \(x_1,\dots , x_n \in ^d\)  be a set of points and \(p \in [1, 2]\) . The set \(S \subset [n]\)  and \(w \colon S \rightarrow _{\ge 0}\)  is an \(\) -strong coreset for \((k, z)\) -clustering in \(\ell _p\)  if for any set of \(k\)  points \(c_1,\dots ,c_{\ell } \in ^d\) ,

i=1n [k]  xi - c pz 1 i S w(i) [k]  xi - c pz.
